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Chapter 9 · Questions · page 44 of 68

Is -3 squared 9 or -9?

Short answerWritten as -3², it is -9, because the square applies to the 3 only. Written as (-3)², it is 9, because the parentheses put the negative inside the square.

levelPre-algebra
standard8.EE.A.1
practiceOrder of operations

An exponent only reaches what is directly under it. In -3², the minus sign sits outside, so you square 3 and then make it negative. Calculators and teachers read it the same way. If you mean the negative number squared, the parentheses are required.

How to use it

  1. Look for parentheses around the negative number.
  2. No parentheses: square the number, then apply the minus.
  3. Parentheses: multiply the negative number by itself.

Example

−32=−(3×3)=−9-3^2 = -(3 \times 3) = -9
(−3)2=(−3)×(−3)=9(-3)^2 = (-3) \times (-3) = 9
−24=−16-2^4 = -16

Where it goes wrong

  • Reading -3² as (-3)². This is one of the most common sign slips in algebra.
  • Typing -3^2 into a calculator and expecting 9.

Related

ExponentsMultiplying and dividing signsThe sign belongs to the term
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